I can't really tell if it's rotting, but it's definitely lacking light. Your little friend does not look happy. If this were mine I would take it out and get all the old soil off. Inspect the roots and check for rot. When you potted this up did you take all the old soil off or did you just leave the old soil on. For me I think it's very important to get all that old soil off when you first repot. For a couple reasons. One you can't inspect the roots properly. Two the soil that usually comes with the plant is not good. It's very peaty. Peat is no bueno for succulents in the long run;). Can retain moisture. On the other hand once peat dries out it becomes like concrete. It's like trying to saturate styrofoam with water. Doesn't work. If the plant looks ok then repot. From what I can see it doesn't look rotten. Just needs more light. Start to acclimate your Echeveria to more light slowly. It will burn if this is done too quickly. Goodluck:). Yes you can try to propagate the healthy leaf:).

The main issue I see is too much sun. The first pic is a Haworthia and that should be put in the shade tbh. It’ll be much happier. Those like less light than most other succulents. Will the extra sun kill it? No, but you can see it looks jaundice. Once you put somewhere protected the Haworthia will turn back to green. If I were to put an Echeveria in the same light as what a Haw likes, that Echeveria would become very etiolated. Not all succulents love to be beat by the sun;). Some grow in shrubby areas beneath other plants. The little cracks I see on your Aloe and Graptoveria ‘Opalina’ are most likely from too much water, but they have scabbed over and one day those leaves will grow out, and be gone. What looks like burn marks is exactly what they are, burned from the sun. I have an Echeveria ‘Lola’ that looks like yours right now, it’s almost white from the sun. Move these guys to morning sun and afternoon shade. If you can;). If not you can get objects to block some of the plants. I have some Sempervivum that will fry in my sun. No matter how slowly I acclimate;). So I just put a couple pots in front to protect them. Hopefully that helps. There’s also shade cloth that people use, but I have zero experience with those;). Tbh they don’t look too bad, easy fix. They’re not rotting or turning to mush, just a little sunburnt. It happens to me every year. Even if I know better there will always be a plant or two I will forget about and they end up like yours;).

I think you should cut higher up because there looks like more rot farther up on the stem. The flesh of the stem when you cut should be clean, no brown marks. Make sure to use a clean sharp knife. I also drew another line where you could cut on the rooted part. If you want give the rooted part a try. After you cut, pot up into a fast draining mix like 50% rinsed strained perlite or pumice and 50% cactus mix, and water in about 5 days. Be patient and you may get baby plants. Goodluck;). You may pop off a leaf or two, but that’s fine because you could just set those on top of some mix. Eventually roots should come out.

There are quite a few things that went wrong here! Let me explain: Succulents come from very dry environments in which they get lots of sun, and very little water. This is why they have thicker leaves than other plants: they store water to use during the times that they won't get rain. They are drought-tolerant, because they can survive long periods without water, but die very quickly if they receive too much water too frequently, have poor drainage, or the soil they are planted in does not dry out quickly enough. Your succulent's soil lacks aeration: it looks like basic potting soil, which holds too much water for succulents. This is water-retentive soil. You want a fast-draining soil for succulents. Solution: You can improve your current soil by adding at least 50% perlite or pumice. You can also buy soil made specifically for cacti&succulents, which should have lots of grittiness to it to make it less water-retentive. Avoid anything with peat moss in it, which is a water-retentive ingredient. Your succulent was overpotted. This means that its root ball is very small in comparison to its pot. When you watered your plant, its roots were surrounded with much more water than they could use. Solution: Next time, try to choose a pot that is only 1 inch bigger than your plant's root ball. Your succulent did not receive sufficient light. I can't tell what kind of succulent you had, but a large majority of succulents prefer full sun, as that's what they receive in their native environments. This lack of sun contributed to your soggy soil, as your succulent did not have any assistance from sunlight to help dry it out. Solution: Look up the specific lighting needs of the next succulent you care for, and follow those. Lack of lighting won't kill most plants on its own, but can cause "etiolation" (when a plant grows long, weak stems in an attempt to find light). You watered far too often. A very important thing for beginners to learn is this: do not water "every few days" or "x times per week" etc. Do not water on a schedule! Water when your plant needs it. Solution: Succulents only need to be watered when their soil is completely dry. Get a wooden dowel, and insert it into the soil. If the dowel comes out dry, your succulent needs water! If it comes out damp, with some soil sticking to it, do not water. Finally, your succulent did not have a drainage hole. This is absolutely non-negotiable in keeping succulents. You MUST pick a pot with a drainage hole, or there is nowhere for the excess water to go, and the soil stays soggy. Solution: Choose a pot with a drainage hole. When it's time to water your succulent, water thoroughly, until water drains from the bottom. Let all of the excess water drain out. Your succulent died from root rot caused by all of these factors. Don't be discouraged, though! Keep all of these things in mind. Caring for plants is a simple matter of learning what they need and giving them that to the best of your ability. :)